Linear representation theory of groups of order 120

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This article gives specific information, namely, linear representation theory, about a family of groups, namely: groups of order 120.
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The three non-solvable groups

There are three non-solvable groups of order 120, whose linear representation theory deserves special mention:

Group Quasisimple group? Almost simple group? Linear representation theory
symmetric group:S5 No Yes linear representation theory of symmetric group:S5
special linear group:SL(2,5) Yes No linear representation theory of special linear group:SL(2,5)
direct product of A5 and Z2 No No linear representation theory of direct product of A5 and Z2

Degrees of irreducible representations

FACTS TO CHECK AGAINST FOR DEGREES OF IRREDUCIBLE REPRESENTATIONS OVER SPLITTING FIELD:
Divisibility facts: degree of irreducible representation divides group order | degree of irreducible representation divides index of abelian normal subgroup
Size bounds: order of inner automorphism group bounds square of degree of irreducible representation| degree of irreducible representation is bounded by index of abelian subgroup| maximum degree of irreducible representation of group is less than or equal to product of maximum degree of irreducible representation of subgroup and index of subgroup
Cumulative facts: sum of squares of degrees of irreducible representations equals order of group | number of irreducible representations equals number of conjugacy classes | number of one-dimensional representations equals order of abelianization
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